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In this paper, we address a question posed by L. Shapiro regarding algebraic and/or combinatorial characterizations of the elements of order 2 in the Riordan group. We present two classes of combinatorial matrices having pseudo-order 2. In one class, we find generalizations of Pascal's triangle and use some special cases to discover and prove interesting(More)
The purpose of this paper is twofold. As the first goal, we show that three different classes of random walks are counted by the Pell numbers. The calculations are done using a convenient technique that involves the Riordan group. This leads to the second goal, which is to demonstrate this convenient technique. We also construct bijections among Pell,(More)
Riordan matrix methods and manipulation of various generating functions are used to find curious relations among the Catalan, central binomial, and RNA generating functions. In addition, the Wilf-Zeilberger method is used to find identities where the gamma function and Catalan numbers are expressed in terms of the Gauss hy-pergeometric function. As a(More)
Riordan matrix methods and properties of generating functions are used to prove that the entries of two Catalan-type Riordan arrays are linked to the Chebyshev poly-nomials of the first kind. The connections are that the rows of the arrays are used to expand the monomials (1/2) (2x) n and (1/2) (4x) n in terms of certain Chebyshev poly-nomials of degree n.(More)
The focus of this Research Experience for Undergraduates (REU) project was on RNA secondary structure prediction by using a lattice walk approach. The lattice walk approach is a combinatorial and computational biology method used to enumerate possible secondary structures and predict RNA secondary structure from RNA sequences. The method uses discrete(More)
Evidence is presented suggesting, for the first time, that the protein foldability metric sigma = (T(theta)-T(f))/T(theta), where T(theta) and T(f) are, respectively, the collapse and folding transition temperatures, could be used also to measure the foldability of RNA sequences. These results provide further evidence of similarities between the folding(More)
Purdue's focus is on visualization sciences, and Rutgers' focus is on data sciences, these two CVADA components are working closely on a number of activities, projects, and programs (Command, Control, and Interoperability Center for Advanced Data Analysis, 2013). Excellence perform critical research and development activities to provide the necessary(More)
Metrics for indirectly predicting the folding rates of RNA sequences are of interest. In this letter, we introduce a simple metric of RNA structural complexity, which accounts for differences in the energetic contributions of RNA base contacts toward RNA structure formation. We apply the metric to RNA sequences whose folding rates were previously determined(More)
The involvement of beta-amyloid (Abeta) in the pathogenesis of Alzheimer's disease (AD) has been well documented. In addition, a significant degree of information has been documented regarding the genetics of Abeta production and aggregation in familial forms of AD (FADs). However, the information regarding the causes or mechanism(s) responsible for Abeta(More)